Public question bank · Class 10 · Mathematics

Class 10 Mathematics - Chapters 1-4

110 original MCQs with answers and worked explanations, aligned with NCERT Class 10 Mathematics: Real Numbers (20), Polynomials (30), Pair of Linear Equations in Two Variables (30), Quadratic Equations (30).

Chapters / topics

Chapter 1: Real Numbers · 20 Chapter 2: Polynomials · 30 Chapter 3: Pair of Linear Equations in Two Variables · 30 Chapter 4: Quadratic Equations · 30

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Chapter 3: Pair of Linear Equations in Two VariablesAll chapters

30 ready questions · 10 per page

11. Chapter 3: Pair of Linear Equations in Two Variables · mcq

For what value of k do $kx+3y=5$ and $2x+6y=9$ have no solution?

Show answer and explanation

Parallel lines require $k/2=3/6$ , so $k=1$ . Doubling $x+3y=5$ gives $2x+6y=10$ , inconsistent with the second constant 9.

12. Chapter 3: Pair of Linear Equations in Two Variables · mcq

Which point is the intersection of $x+y=1$ and $x-y=5$ ?

$(-3,2)$

$(3,-2)$

$(-2,3)$

$(2,-1)$

Show answer and explanation

$(3,-2)$

Adding gives $2x=6$ , so $x=3$ . Then $y=1-3=-2$ . The intersection is $(3,-2)$ .

13. Chapter 3: Pair of Linear Equations in Two Variables · mcq

Solve $x+2y=4$ and $2x-y=-2$ .

$x=-2,\ y=3$

$x=4,\ y=0$

$x=0,\ y=2$

$x=2,\ y=1$

Show answer and explanation

$x=0,\ y=2$

Double the first equation to obtain $2x+4y=8$ . Subtracting $2x-y=-2$ gives $5y=10$ , so $y=2$ and $x=0$ .

14. Chapter 3: Pair of Linear Equations in Two Variables · mcq

Solve $x+y=0$ and $x-y=8$ .

$x=-4,\ y=4$

$x=8,\ y=0$

$x=0,\ y=-8$

$x=4,\ y=-4$

Show answer and explanation

$x=4,\ y=-4$

Adding gives $2x=8$ , so $x=4$ . Since $x+y=0$ , $y=-4$ .

15. Chapter 3: Pair of Linear Equations in Two Variables · mcq

The sum of two numbers is 27 and their difference is 5. What is the larger number?

Show answer and explanation

Let the larger number be $x$ and the smaller be $y$ . Adding $x+y=27$ and $x-y=5$ gives $2x=32$ , so $x=16$ .

16. Chapter 3: Pair of Linear Equations in Two Variables · mcq

The sum of the digits of a two-digit number is 11. The number is 27 greater than its digit-reversed number. What is the original number?

Show answer and explanation

Let the tens digit be $x$ and the units digit be $y$ . Then $x+y=11$ and $9(x-y)=27$ , so $x-y=3$ . Hence $x=7,y=4$ and the number is 74.

17. Chapter 3: Pair of Linear Equations in Two Variables · mcq

A father is three times as old as his son. Their present ages add up to 48 years. How old is the father?

24 years

40 years

36 years

12 years

Show answer and explanation

36 years

If the son is $s$ years old, the father is $3s$ . Thus $4s=48$ , so $s=12$ and the father is 36 years old.

18. Chapter 3: Pair of Linear Equations in Two Variables · mcq

A father and son have a combined present age of 40 years. Five years ago, the father was five times as old as the son. What is the son's present age?

5 years

8 years

15 years

10 years

Show answer and explanation

10 years

Let their ages be $f,s$ . Then $f+s=40$ and $f-5=5(s-5)$ , so $f-5s=-20$ . Substituting $f=40-s$ gives $60=6s$ , hence $s=10$ .

19. Chapter 3: Pair of Linear Equations in Two Variables · mcq

Two pens and three notebooks cost ₹96. Four pens and three notebooks cost ₹132. What is the cost of one pen?

₹18

₹12

₹20

₹36

Show answer and explanation

₹18

Subtract $2p+3n=96$ from $4p+3n=132$ to get $2p=36$ . Hence one pen costs ₹18; the notebook price is ₹20.

20. Chapter 3: Pair of Linear Equations in Two Variables · mcq

Two adult tickets and three child tickets cost ₹210. Three adult tickets and two child tickets cost ₹240. What is the price of one child ticket?

₹60

₹30

₹40

₹50

Show answer and explanation

₹30

Let prices be $a,c$ . From $2a+3c=210$ and $3a+2c=240$ , eliminate $a$ : $6a+9c=630$ and $6a+4c=480$ . Thus $5c=150$ and $c=30$ .